Computational Statistics

, Volume 33, Issue 2, pp 709–730 | Cite as

Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model

  • Thiago G. Ramires
  • Niel Hens
  • Gauss M. Cordeiro
  • Edwin M. M. Ortega
Original Paper

Abstract

Nonlinear effects between explanatory and response variables are increasingly present in new surveys. In this paper, we propose a flexible four-parameter semi-parametric cure rate survival model called the sinh Cauchy cure rate distribution. The proposed model is based on the generalized additive models for location, scale and shape, for which any or all parameters of the distribution are parametric linear and/or nonparametric smooth functions of explanatory variables. The new model is used to fit the nonlinear behavior between explanatory variables and cure rate. The biases of the cure rate parameter estimates caused by not incorporating such non-linear effects in the model are investigated using Monte Carlo simulations. We discuss diagnostic measures and methods to select additive terms and their computational implementation. The flexibility of the proposed model is illustrated by predicting lifetime and cure rate proportion as well as identifying factors associated to women diagnosed with breast cancer.

Keywords

Cure rate models GAMLSS Long-term survivors P-spline Residual analysis 

Notes

Acknowledgements

The first author acknowledge the financial support of the “Ciência sem Fronteiras” program of CNPq (Brazil) under the process number 200574/2015-9.

Compliance with ethical standards

Conflict of interest

The authors have declared no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Thiago G. Ramires
    • 1
    • 2
  • Niel Hens
    • 2
    • 3
  • Gauss M. Cordeiro
    • 4
  • Edwin M. M. Ortega
    • 5
  1. 1.Department of MathematicsFederal University of Technology - ParanáApucaranaBrazil
  2. 2.Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-Biostat)University of HasseltHasseltBelgium
  3. 3.Centre for Health Economic Research and Modelling Infectious Diseases, Vaccine and Infectious Disease InstituteUniversity of AntwerpAntwerpenBelgium
  4. 4.Department of StatisticsFederal University of PernambucoRecifeBrazil
  5. 5.Department of Exact SciencesUniversity of São PauloSão PauloBrazil

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